Quadratic Programming

Quadratic programming problems are more complex than LP problems, but simpler than general NLP problems. Such problems have only one feasible region with "flat faces" on its surface, but the optimal solution may be found anywhere within the region or on its surface. Frontline's Quadratic Solver uses the Simplex method to determine the feasible region, then uses special methods based on the properties of quadratics to find the optimal solution.

Large QP problems are subject to many of the same considerations as large LP problems: When using a straightforward or "dense" representation as in Frontline's current Quadratic Solver, the amount of memory required increases with the number of variables times the number of constraints, regardless of the model's sparsity. Numerical instabilities can arise in QP problems and may cause more difficulty than in similar-size LP problems. To deal with these issues, Frontline hopes to offer a large-scale sparse quadratic solver in the future.